Skip to main content
SpringerLink
Log in

Tight-Binding Methods

  • Chapter
  • First Online:
Computational Materials Science

  • 2164 Accesses

Abstract

Despite recent major developments in algorithms and computer hardware, the simulation of large systems of particles by ab initio methods is still limited to about a hundred particles. For treating larger systems by molecular dynamics, one can use either tight-binding (TB) or classical molecular- dynamics methods. The TB method has the advantage of being quantum mechanical; therefore one has, in addition to its higher accuracy, information about the electronic structure of the system. In the field of quantum chemistry, other semi-empirical methods, such as MNDO (modified neglect of differential overlap), also exist. These are, in their nature, very similar to Hartree–Fock methods, but the computations of the Hamiltonian and overlap matrix elements are based on semi-empirical formulae.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 79.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 99.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 129.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. J.C. Slater, G.F. Koster, Phys. Rev. 94, 1498 (1954)

    Article  CAS  Google Scholar 

  2. C. Xu, C.Z. Wang, C.T. Chan, K.M. Ho, J. Phys. Condens. Matter 4, 6047 (1992)

    Article  CAS  Google Scholar 

  3. M. Mehl, D. Papaconstantopoulos, Phys. Rev. B 54, 4519 (1996)

    Article  CAS  Google Scholar 

  4. F. Liu, Phys. Rev. B 52, 10677 (1995)

    Article  CAS  Google Scholar 

  5. D. Porezag, Th Frauenheim, Th Köhler, G. Seifert, R. Kaschner, Phys. Rev. B 51, 12947 (1995)

    Article  CAS  Google Scholar 

  6. A. Taneda, K. Esfarjani, Z.Q. Li, Y. Kawazoe, Comput. Mat. Sci. 9, 343 (1998)

    Google Scholar 

  7. W.A. Harrison, Electronic Structure and the Properties of Solids (Dover, New York, 1980)

    Google Scholar 

  8. M. Menon, K.R. Subbaswamy, Phys. Rev. Lett. 67, 3487 (1991); Int. J. Mod. Phys. 6, 3839 (1992)

    Article  CAS  Google Scholar 

  9. A.P. Sutton, M.W. Finnis, D.G. Pettifor, Y. Ohta, J. Phys. C. 21, 35 (1988)

    Article  Google Scholar 

  10. P.W. Anderson, Phys. Rev. Lett. 21, 13 (1968); Phys. Rev. 181, 25 (1969)

    Article  Google Scholar 

  11. A.P. Horsefield, Phys. Rev. B 56, 6594 (1997). References therein

    Article  Google Scholar 

  12. V. Heine, Solid State Phys. 35, 47 (1980); D.W. Bullet, Solid State Phys. 35, 173 (1980)

    Google Scholar 

  13. M. Foulkes, R. Haydock, Phys. Rev. B 39, 12520 (1989)

    Article  CAS  Google Scholar 

  14. I. Kwon, R. Biswas, C.Z. Wang, K.M. Ho, C.M. Soukoulis, Phys. Rev. B 49, 7242 (1994)

    Article  CAS  Google Scholar 

  15. L. Goodwin, A.J. Skinner, D.G. Pettifor, Europhys. Lett. 9, 701 (1989)

    Article  CAS  Google Scholar 

  16. M.S. Tang, C.Z. Wang, C.T. Chan, K.M. Ho, Phys. Rev. B 53, 979 (1996)

    Article  CAS  Google Scholar 

  17. M.C. Payne, M.P. Teter, D.C. Allan, T.A. Arias, J.D. Joannopoulos, Rev. Mod. Phys. 64, 1045 (1992)

    Article  CAS  Google Scholar 

  18. X.P. Li, R.W. Nunes, D. Vanderbilt, Phys. Rev. B 47, 10891 (1993)

    Article  CAS  Google Scholar 

  19. M.S. Daw, Phys. Rev. B 47, 10895 (1993)

    Article  CAS  Google Scholar 

  20. P. Ordejon, D.A. Drabold, R.M. Martin, M.P. Grumbach, Phys. Rev. B 51, 1456 (1995)

    Article  CAS  Google Scholar 

  21. W. Kohn, Phys. Rev. Lett. 76, 3168 (1996)

    Article  CAS  Google Scholar 

  22. R.W. Nunes, D. Vanderbilt, Phys. Rev. B 50, 17611 (1994)

    Article  CAS  Google Scholar 

  23. W. Hierse, E.B. Stechel, Phys. Rev. B 50, 17811 (1994)

    Article  CAS  Google Scholar 

  24. J.M. Millam, G.E. Scuseria, J. Chem. Phys. 106, 5569 (1997)

    Article  CAS  Google Scholar 

  25. S. Goedecker, L. Colombo, Phys. Rev. Lett. 73, 122 (1994); S. Goedecker, M. Teter, Phys. Rev. B 51, 9455 (1995)

    Article  CAS  Google Scholar 

  26. R. Baer, M. Head-Gordon, J. Chem. Phys. 107, 10003 (1997)

    Article  CAS  Google Scholar 

  27. R. Baer, M. Head-Gordon, Phys. Rev. B 58, 15296 (1998)

    Article  CAS  Google Scholar 

  28. R. Haydock, V. Heine, M.J. Kelly, J. Phys. Chem. 5, 2845 (1972); R. Haydock, Solid State Phys. 35, 215 (1980)

    Google Scholar 

  29. D.R. Bowler, M. Aoki, C.M. Goringe, A.P. Horsefield, D.G. Pettifor, Model. Sim. Matls. Sci. Eng. 5, 199 (1997)

    Article  CAS  Google Scholar 

  30. D. Tomańek, M. Schlüter, Phys. Rev. B 54, 4519 (1986); Phys. Rev. Lett. 65, 1306 (1991)

    Google Scholar 

  31. M. Teter, Phys. Rev. B 48, 5031 (1993). References therein

    Article  CAS  Google Scholar 

  32. K. Ohno, Theor. Chim. Acta 2, 219 (1964); G. Klopman, J. Am. Chem. Soc. 86, 4450 (1964)

    Google Scholar 

  33. P. Fulde, Electron Correlations in Molecules and Solids, vol. 100. Solid-State Series (Springer, Berlin, 1993), p. 151

    Book  Google Scholar 

  34. C.G. Broyden, Math. Comput. 19, 577 (1965); D. Vanderbilt, S.G. Louie, Phys. Rev. B 30, 6118 (1984)

    Google Scholar 

  35. K. Esfarjani, Y. Kawazoe, J. Phys. Condens. Matter 10, 8257 (1998)

    Article  CAS  Google Scholar 

  36. J. Guevara, F. Parisi, A.M. Llois, M. Weissmann, Phys. Rev. B 55, 13283 (1997)

    Article  CAS  Google Scholar 

  37. P. Villase\(\tilde{\rm n}\)or-Gonzales, J. Dorantes-Dávila, H. Dreyssé, G.M. Pastor, Phys. Rev. B 55, 15084 (1997)

    Article  Google Scholar 

  38. J. Dorantes-Dávila, H. Dreyssé, G.M. Pastor, Phys. Rev. B 55, 15033 (1997)

    Article  Google Scholar 

  39. Y. Hashi, K. Esfarjani, S. Itoh, S. Ihara, Y. Kawazoe, Trans. Mat. Res. Soc. Jpn. 20, 486 (1996)

    Google Scholar 

  40. K. Esfarjani, Y. Hashi, S. Itoh, S. Ihara, Y. Kawazoe, Z. Phys. D 41, 73 (1997)

    Google Scholar 

  41. S. Saito, S. Okada, S. Sawada, N. Hamada, Phys. Rev. Lett. 75, 685 (1995)

    Article  CAS  Google Scholar 

  42. J. Onoe, K. Takeuchi, Phys. Rev. B 54, 6167 (1996)

    Article  CAS  Google Scholar 

  43. K. Esfarjani, Y. Hashi, J. Onoe, K. Takeuchi, Y. Kawazoe, Phys. Rev. B 57, 223 (1998)

    Article  CAS  Google Scholar 

  44. A.P. Smith, G.F. Bertsch, Phys. Rev. B 53, 7002 (1996)

    Article  CAS  Google Scholar 

  45. P. Giannozzi, W. Andreoni, Phys. Rev. Lett. 76, 4915 (1996)

    Article  CAS  Google Scholar 

  46. G.F. Bertsch, A.P. Smith, K. Yabana, Phys. Rev. B 52, 7876 (1995)

    Article  CAS  Google Scholar 

  47. D. Bakowies, W. Thiel, Chem. Phys. 151, 309 (1991), R.E. Stratton, M. Newton, J. Phys. Chem. 92, 2141 (1988)

    Google Scholar 

  48. P. Giannozzi, S. Baroni, J. Chem. Phys. 100, 8537 (1994)

    Article  CAS  Google Scholar 

  49. D. Tomańek, M. Schlüter, Phys. Rev. Lett. 56, 1055 (1986); Phys. Rev. B 36, 1208 (1987)

    Google Scholar 

  50. R. Biswas, D.R. Hamann, Phys. Rev. Lett. 55, 2001 (1985); Phys. Rev. B 36, 6434 (1987)

    Google Scholar 

  51. K. Raghavachari, V. Logovinsky, Phys. Rev. Lett. 55, 2853 (1985); K. Raghavachari, J. Chem. Phys. 83, 3520 (1985); J. Chem. Phys. 84, 5672 (1986); K. Raghavachari, C.M. Rohlfing, Chem. Phys. Lett. 143, 428 (1988); J. Chem. Phys. 89, 2219 (1988)

    Article  CAS  Google Scholar 

  52. M.R. Pederson, A.A. Quong, Phys. Rev. Lett. 74, 2319 (1995)

    Article  CAS  Google Scholar 

  53. J.L. Elkind, J.M Alford, F.D. Weiss, R.T. Laaksonen, R.E. Smalley, J. Chem. Phys 87, 2397 (1987); S. Maruyama, L.R. Anderson, R.E. Smalley, J. Chem. Phys 93, 5349 (1990); J.M. Alford, R.T. Laaksonen, R.E. Smalley, J. Chem. Phys. 94, 2618 (1991)

    Google Scholar 

  54. M.F. Jarrold, J.E. Brower, K.M. Creegan, J. Chem. Phys 90, 3615 (1989); M.F. Jarrold, U. Ray, K.M. Creegan, J. Chem. Phys. 93, 224 (1990); U. Ray, M.F. Jarrold, J. Chem. Phys 94, 2631 (1991)

    Google Scholar 

  55. B. Andersen, J.M. Gordon, Phys. Rev. E 50, 4346 (1994)

    Article  Google Scholar 

  56. K. Esfarjani, Y. Hashi, Y. Kawazoe, Nuclus 97 Conference Proceedings, Tsukuba, Japan (1998), p. 403

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, Yokohama National University, Yokohama, Japan

    Kaoru Ohno

  2. Department of Mechanical and Aerospace Engineering, Materials Science and Engineering and Physics, University of Virginia, Charlottesville, VA, USA

    Keivan Esfarjani

  3. New Industry Creation Hatchery Center, Tohoku University, Sendai, Japan

    Yoshiyuki Kawazoe

Authors
  1. Kaoru Ohno
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Keivan Esfarjani
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yoshiyuki Kawazoe
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Kaoru Ohno .

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer-Verlag GmbH Germany, part of Springer Nature

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Ohno, K., Esfarjani, K., Kawazoe, Y. (2018). Tight-Binding Methods. In: Computational Materials Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-56542-1_3

Download citation

Publish with us

Policies and ethics

Search

Navigation